scholarly journals Quantitative Analysis of a Weak Correlation between Complicated Data on the Basis of Principal Component Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tao Pang ◽  
Haitao Zhang ◽  
Liliang Wen ◽  
Jun Tang ◽  
Bing Zhou ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
New Method ◽  
Data Matrix ◽  
Chemical Compositions ◽  
Weak Correlation ◽  
The Difference ◽  
Correlation Information ◽  
Data Matrices

The mining of weak correlation information between two data matrices with high complexity is a very challenging task. A new method named principal component analysis-based multiconfidence ellipse analysis (PCA/MCEA) was proposed in this study, which first applied a confidence ellipse to describe the difference and correlation of such information among different categories of objects/samples on the basis of PCA operation of a single targeted data. This helps to find the number of objects contained in the overlapping and nonoverlapping areas of ellipses obtained from PCA runs. Then, a quantitative evaluation index of correlation between data matrices was defined by comparing the PCA results of more than one data matrix. The similarity and difference between data matrices was further quantified through comprehensively analyzing the outcomes. Complicated data of tobacco agriculture were used as an example to illustrate the strategy of the proposed method, which includes rich features of climate, altitude, and chemical compositions of tobacco leaves. The number of objects of these data reached 171,516 with 14, 4, and 5 descriptors of climate, altitude, and chemicals, respectively. On the basis of the new method, the complex but weak relationship between these independent and dependent variables were interestingly studied. Three widely used but conventional methods were applied for comparison in this work. The results showed the power of the new method to discover the weak correlation between complicated data.

scholarly journals Convex combination of data matrices: PCA perturbation bounds for multi-objective optimal design of mechanical metafilters

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giorgio Gnecco ◽  
Andrea Bacigalupo
Keyword(s):  
Principal Component Analysis ◽  
Optimization Problems ◽  
Convex Combination ◽  
Principal Component ◽  
Component Analysis ◽  
Data Matrix ◽  
Matrix Perturbation ◽  
Perturbation Bounds ◽  
Multi Objective ◽  
Data Matrices

<p style='text-indent:20px;'>In the present study, matrix perturbation bounds on the eigenvalues and on the invariant subspaces found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems – e.g., those arising in the design of mechanical metamaterial filters – is also discussed, together with possible extensions.</p>

Principal component analysis of substituent constants

1990 ◽  
Vol 55 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Drahomír Hnyk
Keyword(s):  
Principal Component Analysis ◽  
Inductive Effect ◽  
Resonance Effect ◽  
Principal Component ◽  
Component Analysis ◽  
Total Variance ◽  
Data Matrix ◽  
Cumulative Proportion ◽  
Two Factors ◽  
Substituent Constants

The principal component analysis has been applied to a data matrix formed by 7 usual substituent constants for 38 substituents. Three factors are able to explain 99.4% cumulative proportion of total variance. Several rotations have been carried out for the first two factors in order to obtain their physical meaning. The first factor is related to the resonance effect, whereas the second one expresses the inductive effect, and both together describe 97.5% cumulative proportion of total variance. Their mutual orthogonality does not directly follow from the rotations carried out. With the help of these factors the substituents are divided into four main classes, and some of them assume a special position.

scholarly journals Deteksi Formalin Pada Buah Tomat (Lycopersicum esculentum Mill) Dengan Teknologi Hidung Elektronik (Electronic Nose)

2019 ◽  
Vol 4 (2) ◽  
pp. 359-366
Author(s):  
Irfan Maibriadi ◽  
Ratna Ratna ◽  
Agus Arip Munawar
Keyword(s):  
Principal Component Analysis ◽  
Electronic Nose ◽  
Principal Component ◽  
Component Analysis ◽  
Lycopersicum Esculentum ◽  
Olfactory Ability ◽  
Pca Method ◽  
The Difference ◽  
Electronic Nose Technology

Abstrak,  Tujuan dari penelitian ini adalah mendeteksi kandungan dan kadar formalin pada buah tomat dengan menggunakan instrument berbasis teknologi Electronic nose. Penelitian ini menggunakan buah tomat yang telah direndam dengan formalin dengan kadar 0.5%, 1%, 2%, 3%, 4%, dan buah tomat tanpa perendaman dengan formalin (0%). Jumlah sampel yang digunakan pada penelitian ini adalah sebanyak 18 sampel. Pengukuran spektrum beras menggunakan sensor Piezoelectric Tranducer. Klasifikasi data spektrum buah tomat menggunakan metode Principal Component Analysis (PCA) dengan pretreatment nya adalah Gap Reduction. Hasil penelitian ini diperoleh yaitu: Hidung elektronik mulai merespon aroma formalin pada buah tomat pada detik ke-8.14, dan dapat mengklasifikasikan kandungan dan kadar formalin pada buah tomat pada detik ke 25.77. Hidung elektronik yang dikombinasikan dengan metode principal component analysis (PCA) telah berhasil mendeteksikandungan dan kadar formalin pada buah tomat dengan tingkat keberhasilan sebesar 99% (PC-1 sebesar 93% dan PC-2 sebesar 6%). Perbedaan kadar formalin menjadi faktor utama yang menyebabkan Elektronik nose mampu membedakan sampel buah tomat yang diuji, karena semakin tinggi kadar formalin pada buah tomat maka aroma khas dari buah tomat pun semakin menghilang, sehingga Electronic nose yang berbasis kemampuan penciuman dapat membedakannya.Detect Formaldehyde on Tomato (Lycopersicum esculentum Mill) With Electronic Nose TechnologyAbstract, The purpose of this study is to detect the contents and levels of formalin in tomatoes by using instruments based on Electronic nose technology. This study used tomatoes that have been soaked in formalin with a concentration of 0.5%, 1%, 2%, 3%, 4%, 5% and tomatoes without soaking with formalin (0%). The samples in this study were 18 samples. The measurements of the intensity on tomatoes aroma were using Piezoelectric Transducer sensors. The classification of tomato spectrum data was using the Principal Component Analysis (PCA) method with Gap Reduction pretreatment. The results of this study were obtained: the Electronic nose began to respond the smell of formalin on tomatoes at 8.14 seconds, and it could classify the content and formalin levels in tomatoes at 25.77 seconds. Electronic nose combined with the principal component analysis (PCA) method have successfully detected the content and levels of formalin in tomatoes with a success rate at 99% (PC-1 of 93% and PC-2 of 6%). The difference of grade formalin levels is the main factor that causes Electronic nose to be able to distinguish the tomato samples tested, because the higher of formalin content in tomatoes, the distinctive of tomatoes aroma is increasingly disappearing. Thereby, the Electronic nose based on  the olfactory ability can distinguish them. 

scholarly journals A new method for selecting sites for soil sampling, coupling global weighted principal component analysis and a cost-constrained conditioned Latin hypercube algorithm

MethodsX ◽  
2019 ◽  
Vol 6 ◽  
pp. 284-299
Author(s):  
Kwabena Abrefa Nketia ◽  
Stephen Boahen Asabere ◽  
Stefan Erasmi ◽  
Daniela Sauer
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Soil Sampling ◽  
New Method ◽  
Latin Hypercube ◽  
Weighted Principal Component

scholarly journals SVD-based principal component analysis of geochemical data

2005 ◽  
Vol 3 (4) ◽  
pp. 731-741 ◽  
Author(s):  
Petr Praus
Keyword(s):  
Principal Component Analysis ◽  
Euclidean Distance ◽  
Principal Component ◽  
Component Analysis ◽  
Data Matrix ◽  
Geochemical Data ◽  
Average Group ◽  
Testing Data ◽  
Value Decomposition ◽  
Geochemical Variables

AbstractPrincipal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.

RECOGNITION OF SMILING FACES USING NEURAL NETWORKS AND SPCA

2004 ◽  
Vol 04 (02) ◽  
pp. 153-163 ◽  
Author(s):  
MIYOKO NAKANO ◽  
FUMIKO YASUKATA ◽  
MINORU FUKUMI
Keyword(s):  
Neural Networks ◽  
Principal Component Analysis ◽  
High Speed ◽  
Principal Component ◽  
Component Analysis ◽  
Research Field ◽  
A Value ◽  
Large Matrix ◽  
The Difference ◽  
The Cost

Research on "man-machine interface" has increased in many fields of engineering and its application to facial expressions recognition is expected. The eigenface method by using the principal component analysis (PCA) is popular in this research field. However, it is not easy to compute eigenvectors with a large matrix if the cost of calculation when applying it for time-varying processing is taken into consideration. In this paper, in order to achieve high-speed PCA, the simple principal component analysis (SPCA) is applied to compress the dimensionality of portions that constitute a face. A value of cos θ is calculated using an eigenvector by SPCA as well as a gray-scale image vector of each picture pattern. By using neural networks (NNs), the difference in the value of cos θ between the true and the false (plastic) smiles is clarified and the true smile is discriminated. Finally, in order to show the effectiveness of the proposed face classification method for true or false smiles, computer simulations are done with real images. Furthermore, an experiment using the self-organisation map (SOM) is also conducted as a comparison.

New Method for Spectral Data Classification: Two-Way Moving Window Principal Component Analysis

2006 ◽  
Vol 60 (8) ◽  
pp. 884-891 ◽  
Author(s):  
Hideyuki Shinzawa ◽  
Shigeaki Morita ◽  
Yukihiro Ozaki ◽  
Roumiana Tsenkova
Keyword(s):  
Principal Component Analysis ◽  
Spectral Data ◽  
Principal Component ◽  
Data Classification ◽  
Component Analysis ◽  
New Method ◽  
Moving Window

Regional Education Development Research Based on Robust Principal Component Analysis

2014 ◽  
Vol 915-916 ◽  
pp. 1361-1366
Author(s):  
Xian Fen Xie ◽  
Bin Hui Wang
Keyword(s):  
Principal Component Analysis ◽  
Basic Education ◽  
Principal Component ◽  
Component Analysis ◽  
Robust Principal Component Analysis ◽  
Education Development ◽  
Comparison Research ◽  
Regional Population ◽  
The Difference ◽  
Regional Education

Education development is the product of endogenous socio-economic; studying on regional differences of education level plays an important role in social and economic development. This paper constructs regional education development index system based on two aspects of basic educational facilities and educational scale, applies robust principal component analysis method to explore education development level differences of China's 31 provinces, and with the traditional principal component analysis for comparison. Research shows that, results obtained by robust principal component analysis is more in line with China's actual situation; the overall level of education is not high and the difference between regions is large; China's basic education is positively correlated with regional economy, while inversely correlated with regional population.

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